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Gross J.L., Tucker T.W. — Topological Graph Theory (Wiley Series in Discrete Mathematics and Optimization)
Gross J.L., Tucker T.W. — Topological Graph Theory (Wiley Series in Discrete Mathematics and Optimization)

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Название: Topological Graph Theory (Wiley Series in Discrete Mathematics and Optimization)

Авторы: Gross J.L., Tucker T.W.

Аннотация:

This definitive treatment written by well-known experts emphasizes graph imbedding while providing thorough coverage of the connections between topological graph theory and other areas of mathematics: spaces, finite groups, combinatorial algorithms, graphical enumeration, and block design. Almost every result of studies in this field is covered, including most proofs and methods. Its numerous examples and clear presentation simplify conceptually difficult material, making the text accessible to students as well as researchers. Includes an extensive list of references to current literature.


Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1987

Количество страниц: 351

Добавлена в каталог: 11.10.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abelian group, canonical form      254
Abelian group, canonical generating set      254
Abelian group, genus of      25
Action of group, fixed point of      182
Action of group, free      21 182
Action of group, natural action of quotient group      270
Action of group, natural action of voltage group      186
Action of group, on graph      21
Action of group, on surface      186
Action of group, orbits of      21 186
Action of group, orientation-preserving subgroup      269
Action of group, pseudofree      186
Action of group, quotient map      21 186
Action of group, quotient space      21 186
Adjacency matrix      4
Adjacent imbeddings      133
Adjacent vertices      4
Alexander's Horned Sphere      100
Alexander's Theorem      179
Algorithm, face-tracing      115
Algorithm, genus      53 149
Algorithm, maximum genus      146
Algorithm, orientability      11
Algorithm, planarity      52
Alternating group      287
Alternative Cayley graph      12 271
Amalgamation of graphs      20
Amalgamation of graphs, genus of      150
Appel and Haken      38
Automorphism of graph      6
Automorphism of graph, fixed-point free      67
Automorphism of graph, preserving edge type      184
Automorphism of graph, respecting rotation      184
Automorphism of graph, reversing rotation      184
Balanced      105
Balanced incomplete (BIBD)      105
Band decomposition of surface      109
Band decomposition of surface, band      109
Band decomposition of surface, bands      109
Band decomposition of surface, ends of      109
Band decomposition of surface, locally oriented      110
Band decomposition of surface, orientability algorithm      111
Band decomposition of surface, orientation-preserving, reversing      110
Band decomposition of surface, reduced      109 2
Basis for graph      54
Battle, Harary, Kodama, Youngs (BHKY) theorem      151
Betti number      135
Block      40
Block design      105
Bouquet of n circles      15
Branched covering      174
Branched covering, branch points      174
Branched covering, deficiency of      175
Branched covering, number of sheets      175
Branched covering, prebranch points      174
Branched covering, regular      186
Cartesian product of graphs      19
Cartesian product of graphs, genus of      155
Cayley color graph      10
Cayley graph      10
Cayley graph for      10ff
Cayley graph for crystallographic      277
Cayley graph for current      194ff
Cayley graph of small genus      283ff
Cayley graph, alternative      12 271
Cayley graph, imbedding of self-dual      208
Cayley graph, imbedding of strongly symmetric      264
Cayley graph, irredundant      304
Cayley graph, left translation      1 3
Cayley graph, symmetric      264ff
Cayley graph, voltage      5 7ff
Cayley graph, weakly symmetric      264
Cell complex      99
Cellular (2—self) imbedding      100
Chromatic number of graph      37
Chromatic number of surface      37 215
Chromatically critical      217
Co-spectral graphs      7
Coil      226
Coloring of graph      37
Coloring of map      37
Commutator of group elements      29 275
Complete bipartite graph      14
Complete bipartite graph, genus of      210
Complete bipartite graph, maximum genus of      148
Complete graph      10
Complete graph, crosscap number of      223ff
Complete graph, genus of      223
Complete graph, maximum genus of      146
Complex, abstract      97
Complex, ceil      99
Complex, planar 2—complex      117
Composition of graph      210
Composition of graph, triangular imbedding for      210
Connected      8
Connected, component      18
Connected, k-connected      40
Connected, k-edge-connected      145
Covering      23 72
Covering transformations of      187
Covering, branched      182ff
Covering, folded      175
Covering, irregular      72ff
Covering, projection      23 72
Covering, regular      23 75 187
Covering, space      23 75
Covering, wrapped      207
Crosscap      26
Crosscap, number of graph      133ff
Crosscap, range      133ff
Crosscap, relation to genus      137ff
Crossing number for      214
Cube (n-cube)      19
Cube (n-cube), crosscap number of      159
Cube (n-cube), genus of      159
Current assignment      194
Current graph (ordinary)      194ff
Current graph, derived graph of      206
Current graph, derived imbedding of      194
Current graph, dual      206
Current graph, edge types of      199
Current graph, natural projection for      206
Current graph, nonorientable      198ff
Current graph, orientable      194
Current graph, reversed comer of      199
Current group      194
Cutpoint      40
Cycle (rt-cycle)      8
Cycle, rank      135
Cycle, space      54
Cycle, structure of permutation      83
Deficicncy of branch point      175
Deficicncy of graph      143
Deficicncy of spanning tree      143
Dihedral group      285
Dihedral group, presentation for      285
Disk sum of two surfaces      1 31
Distance between vertices      36
dodecahedron      19
Double-cover conjecture      46
Dual, graph      31 116
Dual, imbedding      31 116
Dual, plus-direction of edge.      202
Dual, voltage graph      204
Duality      31 116
Duality, current-voltage      202
Edge, coloring of graph      156
Edge, contraction      39
Edge, direction (plus, minus)      4
Edge, loop      4
Edge, proper      4
Edge, saturated color      156
Edge-deletion surgery      124
Edgeinitial, terminal vertices of      4
Euclidean, space group      276ff
Euclidean, triangle group      280
Euler characteristic of cellular imbedding {relative)      121
Euler characteristic of surface      27 1 30
Euler characteristic, equation      27
Euler characteristic, formula      27
Eulerian, circuit      34
Eulerian, graph      34
Face      100
Face, Tracing Algorithm      115
Factor (n-factor)      35
Factorable (n-factorable)      35
Five-color theorem      219
Folded covering      175
Four — Color theorem      38 215
Fruchfs theorem      70
Fundamental, group of graph      92
Fundamental, semigroup of graph      92
Genus of graph      29 132
Genus of group      93 249ff
Genus of surface      29
Genus, abelian      249ff
Genus, average.      147
Genus, distribution      147
Genus, infinite      249
Genus, maximum      132
Genus, minimum      132
Genus, nonorientable (crosscap number)      29
Genus, range      132
Genus, strongly symmetric      264
Genus, symmetric      264
girth      29
Glide      276
Graph      1
Graph, adjacency matrix      4
Graph, amalgamation      20
Graph, automorphism      6
Graph, bipartite      14
Graph, cartesian product      19
Graph, edge set      1
Graph, edge-complement      19
Graph, group      6
Graph, homeomorphic      18
Graph, incidence matrix      3
Graph, induced      17
Graph, isomorphism      5
Graph, map      5
Graph, regular (n-regular)      13
Graph, simplicial (simple)      1
Graph, spanning      16
Graph, subdivision      18
Graph, subgraph      16
Graph, suspension (join)      20
Graph, topological representation      17
Graph, vertex set      1
Graphical regular representation for group      72
Group, abelian      254
Gustin's current graphs      193
Hadwiger conjecture      40
Hajos conjecture      41
Hamiltonian cycle      35
Hamiltonian graph      35
Handle decomposition      109
Hauptvermutung.      98
Heawood, inequality      215ff
Heawood, irregular cases      224ff
Heawood, nonorientable      215
Heawood, number      215ff
Heawood, problem irregular cases      224ff
Heawood, problem orientable      215
Heawood, problem regular cases      224ff
Heawood, regular cases      224ff
Heffter, Lothar      191
Hurwitz's theorem      296
Hurwitz's theorem, refined      298
Hypergraph      97
icosahedron      41
Imbedding, adjacent      133
Imbedding, boundary walk of      101
Imbedding, cellular(2—cell)      100
Imbedding, crosscap range      132
Imbedding, distribution      132
Imbedding, dual      31 116
Imbedding, equivalent      101
Imbedding, Euler characteristic range      148
Imbedding, face (region) of      26 100
Imbedding, genus range      132
Imbedding, quadrilateral      27
Imbedding, side of      26 101
Imbedding, triangular      27
Imbedding, weakly equivalent (congruent)      102
Interpolation theorem, nonorientable      135
Interpolation theorem, orientable.      134
Jordan curve theorem      100
K-metacyclic group      318
Kempe chain      220
Kirchoff voltage law(KVL)      166
KirchofT current law(KCL)      196
Klein bottle      26 103
Konigsberg bridge problem      34
Kuratowski graphs      28
Kuratowski graphs for higher genus      53
Kuratowski's theorem      28 42ff
Ladder, circular      59
Lift of face      163
Lift of rotation      162
Lift of walk      62
Line graph      33
Linear map of simplexes      282
Link of vertex      107
Local genus minimum      149
Local voltage group      87 169
Log of circuits      253
longitude      120
Loop      3
Manifold(rt-manifold)      95
Maschke’s classification of genus zero groups      290 314
Meridian      120
mobius      59
Mobius band      25
Octahedron (cocktail-party) graph      20 206
Ordinary voltages      57
Orientability of surface      6 10
Orientability, algorithm for surface      111
Orientability, test for derived surface      170
Orientability, type of edge or walk      110
Orientation of imbedding      106
Orientation of surface      106
Orientation of triangulation      106
Patchwork      155
Patchwork, disjoint      155
Patchwork, even      156
Patchwork, quadrilateral      156
Patchwork, residual faces of      156
Path (n-path)      8
Permutation voltage graph      81
Permutation voltage graph, base graph      81
Permutation voltage graph, derived graph      81
Permutation voltage graph, derived imbedding      166
Permutation voltage graph, face lifting      167
Permutation voltage graph, imbedded      166
Permutation voltage graph, natural projection      81
Petersen graph      21 58 72 86 18f
Petersen graph, generalized      59 3 16
Petersen's theorem      36
Piecewise linear.      282
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